The use of neural networks (NNs) as universal approximators has recently attracted great attention in various problems in physical sciences.
Despite the recent enthusiasm, there are limited studies of interpretable NN methods, which have led to the characterization of neural networks as “black-boxes" which do not provide feedback from a modeling strategy.
A decisive reason for this is the specification of modeling tasks from the deterministic regression point-of-view: \(L_2\)  norms are well-understood and widely utilized in linear least-squares applications. However, this limits the amount of information one can extract from a modeling effort. In contrast, Bayesian models, for e.g., variational inference [1]} and Gaussian process approximations [2]} offer significant flexibility, and may be utilized to assess model and data quality as well as quantify uncertainty under one umbrella.
